CHAMP重力场恢复时域法和空域法比较研究

利用CHAMP数据恢复重力场的解算方法分为时域法和空域法.本文首先介绍了这两种方法恢复CHAMP重力场的基本原理和算法,分析了它们的优缺点.针对空域法中的延拓误差和格网化误差进行了讨论.计算表明:延拓误差中的截断误差部分影响量级约0.001 m2·s-2(均方误差意义下),最大误差仅为0.11 m2·s-2,可完全忽略;延拓误差中的参考重力场模型误差影响随参考场选取的不同而有所差异,整体而言小于0.1 m2·s-2,但最大误差可达1.3 m2·s-2,采用高精度的参考重力场模型能大大减小延拓误差影响.目前最常用的格网化方法包括加权平均方法和最小二乘配置方法,计算表明,利用30天的CHAMP数据进行2°×2°格网化处理,加权平均法的格网化误差在0.13 m2·s-2量级,最大误差可达1.58 m2·s-2,而最小二乘配置法的格网化误差在0.006 m2·s-2量级,最大误差仅为0.15 m2·s-2,明显优于加权平均法.文章最后对时域法和以快速最小二乘配置(FSC)为代表的空域法恢复60阶次的CHAMP重力场的精度进行了比较,结果表明:两种方法的得到的重力场模型精度相差不大,整体而言,时域法略优于空域法.

Comparison of time-wise approach and space-wise approach for CHAMP gravity field recovery

Time-wise approach and space-wise approach are two kinds of methods commonly used for CHAMP gravity field recovery. In this paper, the theories and algorithms of the two approaches are introduced and their advantages and disadvantages are analyzed. The up/downwards continuation error and gridding error of space-wise approach are discussed. The computation implies that the influence of truncation error of up/downwards continuation is about 0.001 m²·s^-2 (in the sense of RMS), the maximum error is only 0.11 m²·s^-2, which can be ignored in CHAMP gravity field recovery. The influence of the reference gravity field error of up/downwards continuation is less than 0.1 m²·s^-2 in general, but the maximum error can reach 1.3 m²·s^-2. To reduce this error, a high-precision gravity field model should be used in the up/downwards continuation. The weighted-means and least square collocation (LSC) are two gridding methods which are commonly used. The computation shows that the gridding error of weight-means method is about 0.13 m²·s^-2, and the maximum error is about 1.58 m²·s^-2 using 30d CHAMP data to form a grid with 2-degree spacing in longitude and latitude. The gridding error of LSC method is about 0.006 m²·s^-2, and the maximum error is about 0.15 m²·s^-2, which shows that it is obviously superior to the weight-means method. Finally, a comparison is made for the time-wise approach and space-wise approach represented by fast spherical collocation (FSC) to recover a 60 degree and order gravity field model using CHAMP data. The results show that the precision of the recovered gravity field model from the time-wise approach is a litter higher than that from the space-wise approach.